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Chapter 1: Problem 25

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$2761 \quad 3857$$

Short Answer

Expert verified
The correct symbol between 2761 and 3857 is \(<\), so it should be written as 2761 < 3857.

Step by step solution

01

Identify the place values of numbers

First, identify the place values of the given numbers. Starting from right (ones place) to left (thousands place), for 2761 it is 1 ones, 6 tens, 7 hundreds, 2 thousands. For 3857, it is 7 ones, 5 tens, 8 hundreds, 3 thousands.
02

Start comparing from the highest place

Keeping in mind the significance of each place value, start comparing the numbers from the highest place value. Here, it is the 'thousands' place. We have 2 in the thousands place for 2761 and 3 in the thousands place for 3857.
03

Place the right symbol

Since 3 is greater than 2, 3857 is greater than 2761. Therefore, the 'less than' symbol (<) must be placed between the numbers like so: 2761 < 3857.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Place Value
Understanding place value is essential in number comparison. Place value refers to the value of each digit in a number, based on its position. In our numeral system, each position represents a power of 10, making the system a base-10 system.
For example:
  • The rightmost digit is in the "ones" place.
  • The next digit to the left is in the "tens" place, followed by "hundreds," "thousands," and so on.
When comparing two numbers, start with the largest place value first. If the numbers differ at any place, the one with the bigger digit in that place is greater. By understanding place values, you can quickly determine which number is larger without having to focus on each individual digit.
Inequalities
Inequalities are mathematical expressions involving symbols that show the relationship between two values. The most common inequality symbols are:
  • "<" for "less than"
  • ">" for "greater than"
  • "鈮�" for "less than or equal to"
  • "鈮�" for "greater than or equal to"
These symbols help us compare two numbers or quantities, indicating what value one has in relation to the other. When using inequalities, always start by determining the place values to know which value is larger or smaller. This ensures accuracy in comparisons.
Greater Than Less Than
The terms "greater than" and "less than" are foundational in comparisons. When comparing two numbers, these terms are used alongside symbols to denote which number is larger or smaller. In the exercise, the numbers 2761 and 3857 need to be compared.
By evaluating the thousands place first, it is clear that 3857 has a larger value than 2761 because 3 in the thousands place is greater than 2. Therefore, the correct symbol to use between the numbers is the "less than" symbol (
  • 2761 < 3857
This ensures clarity in understanding that 2761 is less than 3857. When using these symbols, remember the shape of the symbol points to the smaller number, which can help in retaining the concept.

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